This invention relates to noise generators and, more particularly, to an apparatus and method for generating a noise signal having a specified statistical distribution, such as a Gaussian distribution.
Electronic noise generators have become increasingly important for generating noise that is used for various purposes, for example testing and calibration of electronic equipment, simulations, and electronic games. Digital noise generators are considered particularly useful in that they exhibit inherent repeatability and stability. The generated digital noise may be either used directly or converted to analog noise.
A known digital technique for producing noise having a specified statistical distribution is to generate a group of random or pseudo-random binary bits, and combine the group of bits to obtain a signal having the desired statistical properties. In the copending U.S patent application Ser. No. 945,163, assigned to the same assignee as the present application, there is disclosed a technique for simultaneously generating a group of pseudo-random binary bits and for combining the bits to obtain a noise signal having Gaussian distributed amplitudes, or to obtain a noise signal which occurs at Poisson-distributed intervals. To obtain the Gaussian-distributed noise, a group of N pseudo-random binary bits, generated at each clock pulse by a pseudo-random bit generator, are summed to obtain a sum signal having a value between zero and N. The probability of obtaining any particular sum between zero and N, at a given clock pulse, is binomial, so the distribution of amplitudes of the sum signals, as a function of time, is binomial. The Central Limit Theorem states that as N (the number of binary random variables summed) gets larger, the distribution of sums approaches a Gaussian distribution.
In a digital noise generator, considerations of complexity and cost make it necessary to use a limited number of binary random variables, N, at each clock pulse. This results in the statistical distribution, obtained from the N binary variables, being an approximation of the specified statistical distribution which one desires to obtain. The approximation error is larger for smaller values of N. Accordingly, cost and complexity are necessarily traded off to some degree against the integrity of the obtained statistical distribution.
It is an object of the present invention to set forth a technique for obtaining an improved approximation of a specified statistical distribution which is to be obtained from a limited number of random variables.